Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Complexity-Induced Geometric Reduction: A Holographic Approach to Quantum Measurement

Richard Hale

Published May 23, 2026• 0 citations
Publisher

Abstract

This paper introduces the Geometric Resource Limit Interpretation (GRLI) of quantum mechanics, proposing that wavefunction collapse is an objective, deterministic event triggered when a system's informational complexity exceeds the local holographic capacity of spacetime. By grounding the collapse mechanism in the Bekenstein Bound and Susskind’s holographic complexity framework, GRLI eliminates the coordinate paradoxes of non-relativistic collapse models and achieves Einsteinian covariance. The author outlines three distinct, falsifiable experimental proposals in photonic interferometry and quantum computing to test for non-thermal, complexity-linked dephasing artifacts.

DOI
10.5281/zenodo.20355478

Related papers

Perspectival Holographic Spacetime: Relational Geometry and the Topological Phase Transition of Measurement

Robert Will

The measurement problem in quantum mechanics and the emergence of spacetime in quantum gravity are traditionally treated as distinct structural crises in theoretical physics. This paper proposes a synthesis of Relational Quantum Mechanics (RQM) and the gauge-gravity duality (AdS/CFT) through a framework termed Perspectival Holographic Spacetime (PHS). By abandoning the assumption of an absolute, globally defined bulk geometry, PHS models spacetime as a sheaf of localized, observer-dependent holographic geometries driven by mutual information. To account for the generation of local Riemannian curvature from entanglement networks, we introduce Morphogenetic Quantum Resources (MQR)—the non-stabilizer complexity required to shape spacetime, directly analogous to biological morphogenesis. Under PHS, quantum measurement is formalized not as an objective collapse, but as a topological phase transition and structural localization within the observer's specific emergent reference frame, thereby providing a purely geometric resolution to the Extended Wigner's Friend paradox.

•Jul 2, 2026•0 citations

Geometric Resolution of the Quantum Measurement Problem:\\ Wavefunction Collapse as a Quantitative Topological Phase Transition via Gravitational Spin Reduction

Dimitrios Ropokis

The quantum measurement problem requires a dynamical mechanism to explain the transition from a linear superposition of states to a single definite eigenstate. In this monograph, we present a quantitative geometric resolution by explicitly deriving the Penrose Objective Reduction (OR) hypothesis from the fundamental, microscopic dynamics of Topological Quantum Chromodynamics (Topological QCD). Rather than treating OR as a phenomenological postulate, we model the wavefunction $\Psi$ as a literal topological superposition within the Gravitational Spin Polarization Tensor $\Pi_{ab}$. We demonstrate that a superposition of macroscopically distinct mass states injects localized scalar curvature $R$. By proposing that the exact Lichnerowicz identity bounds the spectral gap proportionally to the gravitational self-energy $\Delta E_G$, we formulate a compelling candidate mechanism for wavefunction collapse at the time scale $\tau = \hbar / \Delta E_G$. Thus, our framework grounds Penrose's model in a fundamental, non-linear spin-network ontology.

•Mar 6, 2026•0 citations

A 5th-Dimensional Geometric Model for Wave-Particle Duality

M Coffey

This paper proposes a synthesis of the ER=EPR conjecture and Kaluza-Klein 5D theory to resolve the observer paradox. We define the wavefunction as a 4D temporal projection of a static 5th-dimensional geometric manifold. We argue that "collapse" is a dimensional phase transition triggered when entanglement reaches a saturation threshold (E=1.0), transitioning the system from a probabilistic 4D state to a deterministic 5D coordinate via an Einstein-Rosen bridge. Unlike standard holographic frameworks or the conventional ER=EPR conjecture which model a higher-dimensional bulk emerging from lower-dimensional boundary entanglement, this framework introduces an uncompactified 5D Kaluza-Klein static manifold as the primary ontology—defining 4D spacetime, linear time, and wavefunction collapse as cross-sectional, top-down projection artifacts of a fixed higher geometry.

•May 2, 2026•0 citations

Objective Thermodynamic Collapse: Resolving the Quantum Measurement Problem via Infodynamic Bandwidth Saturation

Cody Hudock

The quantum measurement problem has persisted largely because standard formalisms require the insertion of an external observer to collapse the wavefunction. This leaves physics without a kinematic mechanism for the actual transition from a continuous superposition to a discrete outcome. We propose here that wavefunction collapse functions as a deterministic thermodynamic phase transition, forced via the finite processing memory of the spatial vacuum. Operating within the Symbiotic Infodynamic Equilibrium (SIE) framework, we model the macroscopic vacuum as a discrete, finite-capacity Face-Centered Cubic (FCC) relational graph. A quantum superposition is evaluated here as an unformatted data-routing state distributed across this lattice. We show that maintaining this coherent spatial distribution imposes a linear infodynamic memory burden on the substrate. As the spatial extent or the mass of the superposed system increases, this informational burden intersects with the intrinsic holographic capacity of the localized state. Setting this microscopic capacity (S_cap proportional to M^-2) equal to the macroscopic Bekenstein-Hawking entropy (S_BH proportional to M^2) derives a first-principles boundary for quantum behavior (M_cut = m_P / sqrt(2)). We structurally redefine observation not as a conscious act of measurement, but as an entanglement-driven mass transfer. When a microscopic system interacts with a macroscopic apparatus, the aggregate mass penalty breaches the local bandwidth limit of the vacuum, thereby forcing a deterministic formatting of the state. This infodynamic bandwidth saturation yields explicit spatial (delta x_max proportional to M^-3) and temporal limits for objective reduction, while predicting a falsifiable discrete Landauer thermal purge detectable via macroscopic optomechanical interferometry.

•Mar 30, 2026•0 citations

On the Unification of Informational Physics

Rainer Kozyra

Building on the frameworks established in On the Physical Consequences of Distinguishability and On the Stability and Collapse of Physical Information, this paper derives quantum state collapse and Einstein field equations from a single variational principle incorporating a holographic information constraint. Following Jacobson’s thermodynamic approach to gravity, I propose that representational capacity — quantified by the Bekenstein bound — constrains both geometric and quantum dynamics. The constraint is formalized using Kolmogorov complexity: quantum states satisfy K(ψ) ≤ Imax(g), where K(ψ) denotes the minimal algorithmic description length. Varying a total action under this constraint yields Einstein equations with an additional stress-energy contribution from information overflow, and a modified Schrödinger equation with a collapse term proportional to excess complexity. The collapse rate emerges as Γ = (c/R) · max(0, K(ψ) − Imax)/Imax, containing no free parameters. This framework suggests quantum collapse and gravitational curvature represent complementary responses to holographic saturation: energy excess induces curvature, information excess induces collapse. The approach makes testable predictions for interference visibility decay as a function of entanglement depth, distinguishable from existing objective collapse models.

•Feb 17, 2026•0 citations

Wavefunction Collapse from Spin^c Holonomy: Paper VII in MEF Series

Dhiren Jashwant MASTER

The quantum measurement problem — the question of why linear, unitary quantum mechanics yields definite measurement outcomes — has remained open since its formulation in 1927. Existing approaches either postulate collapse (Copenhagen), eliminate it (Everett), or parametrise it phenomenologically through free parameters (GRW spontaneous localisation, Penrose objective reduction). None derive it from the geometry of spacetime. This paper demonstrates that wavefunction collapse is a deterministic geometric process: the relaxation of metric tension across the T²/ℤ₂ orbifold sector of the K₈ manifold within the twelve-dimensional Master Equation framework. The metric stiffness S(𝒬) — comprising both the Randall–Sundrum warp factor and the Spin^c gauge flux energy — determines a corrected collapse timescale: where 𝒬 = ω(ψ − ψ̄)² is the Quantum Coherence Dilaton. This formula produces three distinct regimes without free parameters: an isolated electron (𝒬 → 0) maintains coherent superposition for ∼10¹⁶ τ_Pl; macroscopic inert matter collapses on a power-law timescale τ_coll ∝ 1/𝒬 driven by the Spin^c flux; a high-𝒬 system undergoes effectively instantaneous actualisation at the Planck scale (a geometric Zeno effect). The Born probability rule P_i ∝ |ψ_i|² is proved to be preserved exactly under the Spin^c quarter-period holonomy e^{iπ/2}: the phase cancels identically in the modulus squared. The principal falsifiable prediction is a complexity wall — a sharp, non-linear drop in coherence time at a critical system complexity, distinguishable from the smooth exponential decay of standard environmental decoherence. The same Spin^c flux that stabilises the vacuum and yields Λ_eff ≈ 10⁻¹²² M_Pl⁴ (Paper IV) sets the stiffness profile governing collapse.

•Apr 27, 2026•0 citations
This paper introduces the Geometric Resource Limit Interpretation (GRLI) of quantum mechanics, proposing that wavefunction collapse is an objective, deterministic event triggered when a system's informational complexity exceeds the local holographic capacity of spacetime. By grounding the collapse mechanism in the Bekenstein Bound and Susskind’s holographic complexity framework, GRLI eliminates the coordinate paradoxes of non-relativistic collapse models and achieves Einsteinian covariance. The author outlines three distinct, falsifiable experimental proposals in photonic interferometry and quantum computing to test for non-thermal, complexity-linked dephasing artifacts.
The measurement problem in quantum mechanics and the emergence of spacetime in quantum gravity are traditionally treated as distinct structural crises in theoretical physics. This paper proposes a synthesis of Relational Quantum Mechanics (RQM) and the gauge-gravity duality (AdS/CFT) through a framework termed Perspectival Holographic Spacetime (PHS). By abandoning the assumption of an absolute, globally defined bulk geometry, PHS models spacetime as a sheaf of localized, observer-dependent holographic geometries driven by mutual information. To account for the generation of local Riemannian curvature from entanglement networks, we introduce Morphogenetic Quantum Resources (MQR)—the non-stabilizer complexity required to shape spacetime, directly analogous to biological morphogenesis. Under PHS, quantum measurement is formalized not as an objective collapse, but as a topological phase transition and structural localization within the observer's specific emergent reference frame, thereby providing a purely geometric resolution to the Extended Wigner's Friend paradox.
The quantum measurement problem requires a dynamical mechanism to explain the transition from a linear superposition of states to a single definite eigenstate. In this monograph, we present a quantitative geometric resolution by explicitly deriving the Penrose Objective Reduction (OR) hypothesis from the fundamental, microscopic dynamics of Topological Quantum Chromodynamics (Topological QCD). Rather than treating OR as a phenomenological postulate, we model the wavefunction Ψ\PsiΨ as a literal topological superposition within the Gravitational Spin Polarization Tensor Πab\Pi_{ab}Πab​. We demonstrate that a superposition of macroscopically distinct mass states injects localized scalar curvature RRR. By proposing that the exact Lichnerowicz identity bounds the spectral gap proportionally to the gravitational self-energy ΔEG\Delta E_GΔEG​, we formulate a compelling candidate mechanism for wavefunction collapse at the time scale τ=ℏ/ΔEG\tau = \hbar / \Delta E_Gτ=ℏ/ΔEG​. Thus, our framework grounds Penrose's model in a fundamental, non-linear spin-network ontology.
This paper proposes a synthesis of the ER=EPR conjecture and Kaluza-Klein 5D theory to resolve the observer paradox. We define the wavefunction as a 4D temporal projection of a static 5th-dimensional geometric manifold. We argue that "collapse" is a dimensional phase transition triggered when entanglement reaches a saturation threshold (E=1.0), transitioning the system from a probabilistic 4D state to a deterministic 5D coordinate via an Einstein-Rosen bridge. Unlike standard holographic frameworks or the conventional ER=EPR conjecture which model a higher-dimensional bulk emerging from lower-dimensional boundary entanglement, this framework introduces an uncompactified 5D Kaluza-Klein static manifold as the primary ontology—defining 4D spacetime, linear time, and wavefunction collapse as cross-sectional, top-down projection artifacts of a fixed higher geometry.
The quantum measurement problem has persisted largely because standard formalisms require the insertion of an external observer to collapse the wavefunction. This leaves physics without a kinematic mechanism for the actual transition from a continuous superposition to a discrete outcome. We propose here that wavefunction collapse functions as a deterministic thermodynamic phase transition, forced via the finite processing memory of the spatial vacuum. Operating within the Symbiotic Infodynamic Equilibrium (SIE) framework, we model the macroscopic vacuum as a discrete, finite-capacity Face-Centered Cubic (FCC) relational graph. A quantum superposition is evaluated here as an unformatted data-routing state distributed across this lattice. We show that maintaining this coherent spatial distribution imposes a linear infodynamic memory burden on the substrate. As the spatial extent or the mass of the superposed system increases, this informational burden intersects with the intrinsic holographic capacity of the localized state. Setting this microscopic capacity (S_cap proportional to M^-2) equal to the macroscopic Bekenstein-Hawking entropy (S_BH proportional to M^2) derives a first-principles boundary for quantum behavior (M_cut = m_P / sqrt(2)). We structurally redefine observation not as a conscious act of measurement, but as an entanglement-driven mass transfer. When a microscopic system interacts with a macroscopic apparatus, the aggregate mass penalty breaches the local bandwidth limit of the vacuum, thereby forcing a deterministic formatting of the state. This infodynamic bandwidth saturation yields explicit spatial (delta x_max proportional to M^-3) and temporal limits for objective reduction, while predicting a falsifiable discrete Landauer thermal purge detectable via macroscopic optomechanical interferometry.
Building on the frameworks established in On the Physical Consequences of Distinguishability and On the Stability and Collapse of Physical Information, this paper derives quantum state collapse and Einstein field equations from a single variational principle incorporating a holographic information constraint. Following Jacobson’s thermodynamic approach to gravity, I propose that representational capacity — quantified by the Bekenstein bound — constrains both geometric and quantum dynamics. The constraint is formalized using Kolmogorov complexity: quantum states satisfy K(ψ) ≤ Imax(g), where K(ψ) denotes the minimal algorithmic description length. Varying a total action under this constraint yields Einstein equations with an additional stress-energy contribution from information overflow, and a modified Schrödinger equation with a collapse term proportional to excess complexity. The collapse rate emerges as Γ = (c/R) · max(0, K(ψ) − Imax)/Imax, containing no free parameters. This framework suggests quantum collapse and gravitational curvature represent complementary responses to holographic saturation: energy excess induces curvature, information excess induces collapse. The approach makes testable predictions for interference visibility decay as a function of entanglement depth, distinguishable from existing objective collapse models.
The quantum measurement problem — the question of why linear, unitary quantum mechanics yields definite measurement outcomes — has remained open since its formulation in 1927. Existing approaches either postulate collapse (Copenhagen), eliminate it (Everett), or parametrise it phenomenologically through free parameters (GRW spontaneous localisation, Penrose objective reduction). None derive it from the geometry of spacetime. This paper demonstrates that wavefunction collapse is a deterministic geometric process: the relaxation of metric tension across the T²/ℤ₂ orbifold sector of the K₈ manifold within the twelve-dimensional Master Equation framework. The metric stiffness S(𝒬) — comprising both the Randall–Sundrum warp factor and the Spin^c gauge flux energy — determines a corrected collapse timescale: where 𝒬 = ω(ψ − ψ̄)² is the Quantum Coherence Dilaton. This formula produces three distinct regimes without free parameters: an isolated electron (𝒬 → 0) maintains coherent superposition for ∼10¹⁶ τ_Pl; macroscopic inert matter collapses on a power-law timescale τ_coll ∝ 1/𝒬 driven by the Spin^c flux; a high-𝒬 system undergoes effectively instantaneous actualisation at the Planck scale (a geometric Zeno effect). The Born probability rule P_i ∝ |ψ_i|² is proved to be preserved exactly under the Spin^c quarter-period holonomy e^{iπ/2}: the phase cancels identically in the modulus squared. The principal falsifiable prediction is a complexity wall — a sharp, non-linear drop in coherence time at a critical system complexity, distinguishable from the smooth exponential decay of standard environmental decoherence. The same Spin^c flux that stabilises the vacuum and yields Λ_eff ≈ 10⁻¹²² M_Pl⁴ (Paper IV) sets the stiffness profile governing collapse.